Finite Group Databasebeta

← C2×#28414164 #44442907

Subgroups — C2×#28414164 #44442907

Order 29504.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28414164C2116yesmaximal, direct product factor
2C2×#20301502C212yesmaximal, complemented
3C2×#20301501C213yesmaximal, complemented
4C22×D1844C213yesmaximal, complemented
5C2×D4×D461C216yesmaximal, complemented
6C2×#41×C461C211yesmaximal, characteristic, complemented
7C23×D461C2216yescomplemented
8#20301502C22116yescomplemented
9#20301501C22124yescomplemented
10C2×Dic922C2211yescharacteristic, complemented
11C2×D1844C2216yescomplemented
12C2×D1844C2213yescomplemented
13C2×D1844C22124yescomplemented
14C2×C22⋊D461C2216yescomplemented
15D4×D461C22148yescomplemented
16C2×C4×D461C2216yescomplemented
17#41×C461C2218yescomplemented
18C2×Q8×C461C2211yescharacteristic, complemented
19C2×D4×C461C2213yescomplemented
20C22×C4×C461C2213yescomplemented
21C22×D461—412no—
22C22×D461C2316yes—
23C22×D461C23124yescomplemented
24Dic922C2314yescomplemented
25D1844C23124yescomplemented
26D1844C23112yescomplemented
27C22⋊D461C23124yescomplemented
28C2×Dic461C2312yes—
29C4×D461C23124yescomplemented
30C23×C461C2313yes—
31Q8×C461C2314yescomplemented
32D4×C461C23112yescomplemented
33C2×C4×C461C2311yescharacteristic
34C2×C4×C461C2313yes—
35C2×C4×C461C23112yescomplemented
36C22×C461—26no—
37C22×C461C2416yes—
38C22×C461C2411yescharacteristic
39C2×D461—212no—
40C2×D461—424no—
41C2×D461C24112yes—
42C4×C461C2412yes—
43C4×C461C2416yes—
44Dic461C2414yes—
45C2×C461—26no—
46C2×C461H(5,𝔽2)12yescomplemented
47C2×C461C2511yescharacteristic
48D461—212no—
49C461C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—4611nomaximal, Sylow
51H(5,𝔽2)—46116no—
52C2×#41—4612no—
53C2×#41—4613no—
54C2×#41D46111yescharacteristic, complemented
55C22×D4—4616no—
56C22×D4—4613no—
57C24—4616no—
58#41—46116no—
59#41—46124no—
60#41C2×D46118yescomplemented
61C2×Q8—4611no—
62C2×Q8C2×D46111yescharacteristic, complemented
63C2×D4—4616no—
64C2×D4—46148no—
65C2×D4—4616no—
66C2×D4—4613no—
67C2×D4—46124no—
68C2×D4C2×D46113yescomplemented
69C22×C4—4616no—
70C22×C4C2×D46113yescomplemented
71C23—184412no—
72C23—46124no—
73C23—4616no—
74C23C22×D46113yes—
75Q8—4614no—
76Q8C22×D46114yescomplemented
77D4—46124no—
78D4—46124no—
79D4—46112no—
80D4C22×D461112yescomplemented
81C2×C4—4612no—
82C2×C4—46124no—
83C2×C4C22×D46113yes—
84C2×C4C22×D46111yescharacteristic
85C2×C4C22×D461112yescomplemented
86C22—26no—
87C22—184424no—
88C22—92212no—
89C22—46112no—
90C22C23×D46116yes—
91C22C23×D46111yescharacteristic
92C4—4614no—
93C4C23×D46116yes—
94C4C23×D46112yes—
95C2—26no—
96C2—92212no—
97C2#2841416412yesdirect product factor
98C2C24×D46111yescharacteristic
subgroupG/H
centerC22C23×D461
commutator, cosocleC2×C461C25
FrattiniC2C24×D461
FittingC2×#41×C461C2
socleC22×C461C24
hypercenterC2×#41D461
hypocenterC461C2×H(5,𝔽2)
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #28414164C2direct (N × H)
2. C2×#20301502C2semidirect
3. C2×#20301501C2semidirect
4. C22×D1844C2semidirect
5. C2×D4×D461C2semidirect
6. C2×#41×C461C2semidirect
7. C23×D461C22semidirect
8. #20301502C22semidirect
9. #20301501C22semidirect
10. C2×Dic922C22semidirect
11. C2×D1844C22semidirect
12. C2×D1844C22semidirect
13. C2×D1844C22semidirect
14. C2×C22⋊D461C22semidirect
15. D4×D461C22semidirect
16. C2×C4×D461C22semidirect
17. #41×C461C22semidirect
18. C2×Q8×C461C22semidirect
19. C2×D4×C461C22semidirect
20. C22×C4×C461C22semidirect
23. C22×D461C23semidirect
24. Dic922C23semidirect
25. D1844C23semidirect
26. D1844C23semidirect
27. C22⋊D461C23semidirect
29. C4×D461C23semidirect
31. Q8×C461C23semidirect
32. D4×C461C23semidirect
35. C2×C4×C461C23semidirect
46. C2×C461H(5,𝔽2)semidirect
49. C461C2×H(5,𝔽2)semidirect
54. C2×#41D461semidirect
60. #41C2×D461semidirect
62. C2×Q8C2×D461semidirect
68. C2×D4C2×D461semidirect
70. C22×C4C2×D461semidirect
76. Q8C22×D461semidirect
80. D4C22×D461semidirect
85. C2×C4C22×D461semidirect
97. C2#28414164direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#284141642
C2×#203015022
C2×#203015012
C22×D18442
C2×D4×D4612
C2×#41×C4612
C2×H(5,𝔽2)461